Strapdown inertial navigation systems are frequently used in missiles and aircraft. A state-of-the-art strapdown inertial navigation system has three rotation sensors or gyroscopes (gyros) and three specific force sensors or accelerometers rigidly attached to a supporting vehicle. The gyros are each positioned and oriented to sense angular displacement about one of three defined orthogonal axes attached to the vehicle body and known as the body coordinate system. The accelerometers are each positioned and oriented in a fixed direction relative to the vehicle in order to sense velocity changes (incremental velocities) along the three defined orthogonal axes.
The gyros and accelerometers have fixed relative directions in the body coordinate system. An angular transformation matrix of direction cosines is computed in an attitude integration apparatus. The accelerometer signals, e.g., incremental changes in velocity, in the strapdown body coordinate system are converted in a coordinate transformation computer from that system into corresponding signals in the stabilized navigation coordinate system.
A rotation matrix is created in the attitude integration apparatus to transform vector body-coordinate signals from the body coordinate system of the instruments to the navigation coordinate system. The transformed signals are used to calculate and create signals that are measures of the local geographical position of the vehicle and the direction of the local gravity. The transformation matrix also yields signals that are measures of the angular orientation of the supporting vehicle relative to the navigation coordinate system.
The data used to compute the transformation matrix is sampled at finite periodic intervals, causing the bandwidth of the signals to be limited. When the instruments experience vibrations that occur at frequencies above or near the upper limit of the bandwidth of the transformation, where the response is poor, rectification errors occur in the calculated incremental velocity signals, and the navigation coordinate system signals are degraded. The rectification errors producing such degradation are typified by sculling and coning errors. A faster sampling rate of the instrument signals and/or compensation algorithm(s) may be utilized to improve the transformation of incremental velocity from body coordinates to navigation coordinates, although such methods result in additional cost and/or complexity of design due to additional implementation needed to accomplish the task. In addition, the instruments themselves may exhibit sensitivities to vibration. For example, gyros may falsely indicate a rotational vibration motion in response to a translational vibration motion. Such erroneous signals combined with true rotational motion may cause rectification resulting in severe degradation in the attitude integration.
Iso-inertial iso-modal instrument sensor assemblies and suspension systems have been used to support gyros and accelerometers in strapdown inertial navigation systems. These suspension systems used with the sensor assemblies employ multiple (typically 4 or more) isolators to provide shock and vibration isolation for the sensors. The suspension systems reduce the amount of high frequency vibration energy experienced by the sensors. Cylindrically symmetric isolators, i.e., symmetric about the axial direction, are a convenient design choice because they are relatively easy to manufacture and use. These iso-modal isolator suspension systems provided a significant vibration performance improvement as compared to their predecessors. Such suspension systems, however, may exhibit cross-axis acceleration and rotational coupling, for example, in the presence of vibration. This cross-axis coupling is caused by difference in stiffness in the isolators depending on direction, e.g., the radial stiffness is different from the axial stiffness. When all the isolators are substantially matched to one another, the configuration does not exhibit acceleration to rotation coupling, although radial to axial mismatch causes cross-axis acceleration coupling and cross-axis rotation coupling.
A sensor assembly may be illustrated as a cube that is inherently iso-inertial, such as the cube 101 in FIG. 1, which shows an example of a suspension system using four isolators. The isolators 105 are arranged in a tetrahedral configuration, i.e., the isolators 105 are located at every other corner 107 of the cube. The axes of the isolators 105, e.g., the axial direction, are all parallel to one another. In the example of FIG. 1, the isolator axes are all parallel to a diagonal 103 of the cube. When the isolators 105 have the same axial and radial properties, the three translational eigen-frequencies are the same, the three rotational eigen-frequencies are the same, and the ratio of the rotational to translational frequency is determined strictly from geometric considerations and dimensions.
When the axial stiffness and radial stiffness are not equal, the translational eigen-frequencies separate as do the rotational eigen frequencies. This separation leads to cross-axis translational coupling and cross-axis rotational coupling, which may result in errors in determination of, for example, system attitude, acceleration, velocity, and/or position. There are, however, no cross-coupling terms between translation and rotation.
Accordingly, there is a need for a sensor assembly that utilizes isolators without additional cost and/or complexity of design, yet without cross-axis translational coupling and cross-axis rotational coupling.